First electric currents were brought up, in connection with Oersted's work.
Then electric charges, in connection with electrons.

That may be OK, because most of us are familiar with currents and charges. Currents run electric lights, radios, TVs, clocks and applicances in the home, and "static" electric charge causes papers and clothes to cling together in dry weather. An electric current is essentially the continuous flow of electric charge. This section goes a little further, to the concepts of voltage and of the electric field.

Ohm's law

It is easier to understand electricity if we regard electric charge as a sort of fluid, like water, as scientists did for the first 200 years. Yes, it does consist of individual electrons, but those are so small that any large charge behaves like a continuous fluid. In the same way sand pours like a fluid, and water in a glass is usually regarded as a fluid, even though it consists of individual molecules.

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Using a pump we can push water through a pipe around a closed circuit (top drawing). The rate at which it flows past any point in the pipe--measured in gallons (or liters) per second--depends on the pressure produced by the pump (measured in pounds per square inch, or kilograms per square centimeter). More accurately, it depends on the pressure difference between the entrance to the pipe (left) and the exit from the pipe (right).

The greater the pressure difference, the greater the flow. In addition, given a certain pressure difference, a fatter pipe will carry more water, and a longer one will resist the flow and carry less.

All this mirrors exactly the behavior of the electric fluid.

No pipes here, though: electricity in our homes and appliances usually flows in metal wires, most often of copper. Electrons in a metal can jump from atom to atom, and that way carry negative charge around the circuit.

Like a fluid, they are driven by a kind of electric pressure, known as voltage, because it is measured in units known as volts, named after the Italian scientist Alessandro Volta. An electric battery produces (by a chemical process) a voltage difference V between its two ends, and therefore acts like a pump (bottom drawing).

The electric current I flows from high voltage to low voltage and is measured in units known as Amperes, named for André-Marie Ampere whom we met in section #2. And as with water, we expect that if we increase the driving voltage V, the driven current I will also increase. In fact, the two are pretty much proportional: double the voltage, and you get double the current. That relation is known as Ohm's Law, after Georg Ohm who first formulated it.

Ohm's law (with some extra details concerning the length and thickness of the wire) is usually among the first things taught in electricity classes, and many students therefore view it as one of the fundamental laws of electricity. It isn't. It holds quite well for metal wires, but as will be shown in section #7a, it fails badly in fluorescent tubes--while in space currents exist which flow without any voltage driving them (section #10a).

Electric Fields

One small caution here. By long tradition, the direction of the electric current is defined as the direction in which positive charges move. We may blame Ben Franklin for deciding--by pure guess--what kind of electricity is called "positive" and which "negative." A century later it was found that most electric currents were carried by negative electrons, which move in the opposite direction.

One may therefore argue that the flow direction which should be assigned to electric fluid is really the opposite of what we say it is. But it's much too late to change the old convention.

In our homes, electric currents and effects of electricity are usually channeled along insulated wires.
In 3-dimensional space, on the other hand, electric phenomena tend to spread out. If the way electric current flows in the home resembles water flow in pipes, then in space the flow is often like ocean currents or air motion in the atmosphere, spread out in 2 and even 3 dimensions.

In a wire, voltage depends only on one dimension--on the distance along the wire. In space, every point can have its own voltage. Currents that flow may depend on such voltages, but don't look to Ohm's law for guidance, because the flow of current is primarily dictated by magnetic fields, which makes a difference.

The 3-dimensional voltage distribution is often called the electric field.

Compare:

In a magnetic field the direction of the field is that of the force. If isolated N magnetic poles existed, they too could do so, by moving in the direction of the field, while S poles would move in the opposite direction. The poles at the ends of a compass needle move this way, and thus line up the needle in the direction of the field.

Similarly

An electric field is a region where electric forces can be felt by charged objects, and the direction of the field is the one in which positive charges would move. A positive ion moves in the direction of the field, a negative electron moves in the opposite direction.

If both magnetic and electric fields are present, the motion of ions and electrons gets complicated. That however is left for a later section.